3.2 Additive Synthesis

3.2.1 Theory

3.2.1.1 The harmonic series

The additive series of frequencies (i.e., the series that results from simply adding the same Hertz value repeatedly), which results in a string of intervals of decreasing size, is called the harmonic series:

You can also derive the series by repeating an experiment devised by Pythagoras (ca. 570-510 BCE) in which a string is divided into various proportions:

더하는 식의 주파스 시리즈는 같은 헤르츠 값을 반복적으로 더하는 것을 말한다. 그것은 증가하는 간격의 현의 값을 결정하고. 이런 것을 하모닉 시리즈라 한다.

이런 방식으로 너는 다양한 반복적 하모니 시리즈를 만들어낼수 있는데 피타고라스에 의한 실험이다 이것이. 현은 다양한 비율로 그 길이가 나누어 질 수 있기 때문이지.

The ratios describe the length of the two parts of the string in relation to each other.

When a string is bowed, it doesn't just vibrate as a whole, but also in every whole number proportion:

Here the ratios describe the length of the vibrating section in relation to the length of the entire string.

All of these partial vibrations (called 'partials' or 'harmonics') result in sound as well, so every sound made on a string is in fact already a chord!

The special thing about this chord is that all of its pitches melt together, at least when their relative volumes decrease as the pitches get higher. Every natural sound has overtones. Due to characteristics inherent to the human ear, we hear all of these pitches as just one tone.

In contrast, the upper partials themselves (i.e., the partials above the fundamental) do not have any overtones. An isolated sound without overtones does not exist in nature, but such a thing can be created using electronic means. These are called sine tones, a name that stems from the shape of their waveform:

코드에 대한 특별한 이야기는 그것들의 피치들이 같이 녹아 든다는 것이다. 적어도 그들의 연결되어있는 볼륨이 피치가 높아질수록 증가할때,

모든 자연의 소리는 배음이다 사람귀에 선천적인 특징때문에 우리는 한톤으로 모든 피치를 듣는다.

배음이 안되는 고립된 사운드는 자연에 존재하지 않는다. 그러나 그런 것은 전자적 수단을 사용함로서 만들어질수 있다. 이것은 사인톤이라고 하고,

Physicist Jean Baptiste Joseph Fourier (1768-1830) discovered that every periodic sound can be represented using only sine tones (of different frequency, amplitude, and phase), the sum of which is then identical with the original. Such an analysis and the corresponding mathematical process is called a Fourier analysis and Fourier transformation.

Using this principle, it is possible to create every periodic sound by layering many sine tones, a process called "additive synthesis".

In Pd, as already mentioned, "osc~" can be used to generate a sine tone. Sine tones are a very characteristic sound of electronic music, as they are produced and can only be produced using electronic means.

Using a number of "osc~" objects, whose frequencies form an additive series, you can create a chord based on the overtone series:

물리학자 장밥티스트 요셉포리에는 모든 주기적 사운드는 사인톤만 사용해서 재현할 수 있다는 것을 발견해냈다. 사인톤의 다른 주파수, 증폭, 페이즈로 다양한... 소리 재현, 이걸 포리에 논증, 포리에 변화이라고 부르고..

이런 원리로 많은 사인 톤을 겹쳐서 모든 주기적 사운드를 만들어낼 수 있고. 그것은 더하기식 신스 (합성, 인조)라고 부른다.

위에서 언급했듯이, osc~ 는 사인톤을 발생시키는데 사용하고 사인톤은 전자음악에서 가장 특별한 소리인데, 전자장치를 통해서 만들어질 수있기 때문이지.

osc오브젝트의 숫자를 사용해서, 더하기식 소리 합성의 주파수들을 형성시키고, 배음 시리즈를 베이스로 하는 코드를 만들어 낼 수 있는 것

Typically, amplitudes become smaller as the frequencies get larger in order for the chord to blend better (though for some instruments, it is characteristic for certain partials to be louder than those on either side of them, e.g., the clarinet). The arrangement and relative volumes of overtones determine a sound'scolor. You can also speak of itsspectrum.

The fact that our ears blend the overtones together becomes clear when you change the fundamental frequency:

일반적으로 주파수가 커질 수록 증폭은 작아진다.

기초 프리퀀시를 바꾸어보면 우리 귀가 배음을 어떻게 분명하게 섞는지 알 수 있다.

We'll just use the first eight partials here. (N.B. The term 'partial' includes the fundamental whereas the term 'overtone' does not. In other words, the 1st partial = the fundamental frequency, 2nd partial = 1st overtone, 3rd partial = 2nd overtone, etc.)

Even if you leave out the lower partials, you hear the fundamental frequency as the fundamental when you change it:

Our brain calculates the fundamental based on the remaining spectrum. This non-existent tone is called aresidual tone.

3.2.2 Applications

3.2.2.1 A random klangfarbe (German: sound color)

patches/3-2-2-1-random-color.pd

For the sake of space, this example has been limited to just the first seven partials:

3.2.2.2 Changing one klangfarbe into another

patches/3-2-2-2-colorchange.pd

3.2.2.3 Natural vs. equal-tempered

Let's look at the difference between natural and equal-tempered intervals (first enter the fundamental frequency!):

patches/3-2-2-3-natural-tempered.pd

Showing the difference between natural and equal-tempered tuning in cents (hundredths of a half-step):

You can see here: the 7th partial is 31 cents flatter than the equal-tempered seventh.